Paper 2020/720

Fast algebraic immunity of Boolean functions and LCD codes

Sihem Mesnager and Chunming Tang


Nowadays, the resistance against algebraic attacks and fast algebraic attacks are considered as an important cryptographic property for Boolean functions used in stream ciphers. Both attacks are very powerful analysis concepts and can be applied to symmetric cryptographic algorithms used in stream ciphers. The notion of algebraic immunity has received wide attention since it is a powerful tool to measure the resistance of a Boolean function to standard algebraic attacks. Nevertheless, an algebraic tool to handle the resistance to fast algebraic attacks is not clearly identified in the literature. In the current paper, we propose a new parameter to measure the resistance of a Boolean function to fast algebraic attack. We also introduce the notion of fast immunity profile and show that it informs both on the resistance to standard and fast algebraic attacks. Further, we evaluate our parameter for two secondary constructions of Boolean functions. Moreover, A coding-theory approach to the characterization of perfect algebraic immune functions is presented. Via this characterization, infinite families of binary linear complementary dual codes (or LCD codes for short) are obtained from perfect algebraic immune functions. The binary LCD codes presented in this paper have applications in armoring implementations against so-called side-channel attacks (SCA) and fault non-invasive attacks, in addition to their applications in communication and data storage systems.

Available format(s)
Secret-key cryptography
Publication info
Preprint. MINOR revision.
Boolean function(Fast) Algebraic immunityAlgebraic attackFast algebraic attackFault injection attack Side-channel attackLCD codeReed-Muller code
Contact author(s)
tangchunmingmath @ 163 com
2020-06-16: received
Short URL
Creative Commons Attribution


      author = {Sihem Mesnager and Chunming Tang},
      title = {Fast algebraic immunity of Boolean functions and LCD codes},
      howpublished = {Cryptology ePrint Archive, Paper 2020/720},
      year = {2020},
      note = {\url{}},
      url = {}
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